Breadth-First Search (BFS) generally uses more memory than Depth-First Search (DFS) due to the different data structures and traversal strategies they employ.
Data Structures and Traversal Strategies
BFS uses a Queue:
BFS explores all nodes at the present depth level before moving on to nodes at the next depth level. This requires storing all the nodes at the current level in memory simultaneously.
The queue data structure used in BFS holds all the nodes at the current level, which can grow significantly large, especially in wide graphs with high branching factors. This results in higher memory usage as the queue needs to store all these nodes until they are processed[1][2][10].
DFS uses a Stack:
DFS explores as far as possible along each branch before backtracking. This means it only needs to store the nodes along the current path from the root to the deepest node.
The stack data structure used in DFS holds nodes along the current path, which typically requires less memory compared to BFS. The memory usage is proportional to the depth of the tree (or graph) rather than its breadth[1][2][10].
Memory Usage Comparison
BFS Memory Usage:
The space complexity of BFS is $$O(V)$$, where $$V$$ is the number of vertices. This is because, in the worst case, the queue might need to store all vertices at the current level before moving to the next level[5][17].
For a graph with a high branching factor, the number of nodes at each level can be very large, leading to significant memory consumption.
DFS Memory Usage:
The space complexity of DFS is $$O(bm)$$, where $$b$$ is the branching factor and $$m$$ is the maximum depth of the search. This is because DFS only needs to store the nodes along the current path and their siblings[1][6][12].
In practice, this often results in lower memory usage compared to BFS, especially in graphs where the depth is much smaller than the breadth.
Practical Implications
**BFS is more suitable for finding the shortest path in unweighted graphs because it explores all nodes at the present depth level before moving deeper, ensurin...
